Kudryk Taras (1 results)

Soft cover. Condition: New. 8vo (21.5 cm), 255 pp. Publisher's laminated wrappers. Mathematical Studies: Monograph Series, vol. 3. A textbook-length introduction to nonstandard analysis (NSA), by Wladyslaw Lyantse and Taras Kudryk of Lviv State University, adopting the axiomatic approach developed by Edward Nelson in 1977 rather than Abraham Robinson's original constructive formulation of 1961. The authors regard Nelson's approach as more accessible for learning and applications, and explicitly emphasize the expository and pedagogical character of the work, while incorporating a number of their own results. The seven chapters proceed from the foundations of NSA--standard, internal, and external sets, infinitesimals, the transfer principle, and standardization--to applications in analysis, topology, and functional analysis. Subsequent chapters develop the principles of idealization and standardization, saturation, metric and topological spaces, halos, nearstandard points and shadows, completeness and compactness, and applications to normed and Hilbert spaces. The treatment then extends to linear operators, including nearstandardness conditions, equations involving compact operators, and spectral theorems for compact and noncompact operators, before turning to more specialized forms of standardness for measure and operator spaces. Two appendices treat the passage from internal measure spaces to standard measure spaces and invariant subspaces. With references, index, and list of symbols. A substantial introduction to the methods and applications of nonstandard analysis, particularly useful for readers approaching the subject from classical analysis, topology, and functional analysis.…